Angiogenesis is a critical factor in the progression of malignant disease. Malignant cells overexpress several factors that stimulate the process of vascularization including vascular endothelial growth factor (VEGF) and basic fibroblast growth factor (bFGF). Copper plays a critical role in the process of angiogenesis, acting as a cofactor for the function of several of the key mediators of angiogenesis. The copper-depleting agent tetrathiomolybdate (TM) has been shown to modulate the process of angiogenesis by inhibiting the production of these proangiogenic agents. Both benign and malignant prostate cells express VEGF and bFGF. Recent evidence shows that these molecules are differentially expressed with disease progression in prostate cancer. Urinary VEGF levels correlate with survival in patients with advanced disease indicating the importance of angiogenesis in the progression of this disease. This phase II clinical trial will evaluate the activity of an antiangiogenesis strategy using tetrathiomolybdate to deplete copper in patients with prostate cancer. Assessment of the efficacy of therapy in prostate cancer is difficult due to the predominance of bone metastases in this disease. Prostate specific antigen (PSA) has been shown to be a marker of response following hormonal and cytotoxic therapy for prostate cancer. In a laboratory model, PSA has been shown to inhibit angiogenesis, complicating its use as a response indicator to monitor the effect of therapies aimed at inhibiting angiogenesis. This study will evaluate PSA as an indicator of response to antiangiogenic therapy by correlating levels with evidence of response and progression on computed tomography and bone scan and with the degree of copper depletion measured by serum ceruloplasmin level. The antiangiogenic effects of therapy will also be evaluated by measurement of serum VEGF, bFGF, and interleukins 6 and 8 which are associated with cell proliferation and bone metabolism. The levels of these growth factors/cytokines will then be correlated with the degree of copper depletion, PSA level and response to therapy.